Please review the solutions to Snow Day Problems - Set 3. Then, move on to this set. Be sure to look at the marathon problems and their solutions as well. HAPPY PROBLEM SOLVING!
1. Nidhi buys a chair for $60. She tries to sell it for double the price, but when no one would buy it, she reduced that doubled price by 60%. However, sales tax is 7%. Including tax, what was the final price of the chair?
2. The product of two numbers is 30 and their sum is 16. Express their difference in simplest radical form. (You may use the √ sign in your answer. Copy and paste the sign from here.)
3. If 3 zoogs are worth 5 moogs, and 7 joogs have the same value as 3 moogs, how many joogs would you expect to get in a fair trade for 36 zoogs?
4. Maya is a pilot who regularly flies her small private jet from New York to Chicago. Flying with a 25mph tailwind, the flight takes 3 hours. Flying with a 25mph headwind, the flight takes 4 hours. How far is New York from Chicago?
5. What integer n could be included in the set of integers {6, 11, 13, 7, 14} so that the mean is equal to n + 1?
Don't worry about the names; it's just for encouragement :)
1) $2.52
ReplyDelete2) Still working on it
3) about 38 joogs
4) ?
5) ?
1) $51.36
ReplyDelete2) working on it
3) 36 zoogs would equal 140 joogs
4) working on it
5) 9
Great job, Avanthika and Vishal! I will comment on your answers after I recieve a few more responses.
ReplyDeleteI have posted a new question on the marathon on behalf of Auryan. Go ahead and try that. Have fun!
News about our test day is posted on the Northwestern Website, front page.
ReplyDelete2) 2√34
ReplyDelete4) 600 miles
1. $51.36
ReplyDelete1) $51.36
ReplyDelete2) not sure
3) 108
4) not sure
5) 9
I guess the questions for this week were on the difficult side, so let me know if you need any hints.
ReplyDeleteI am not very sure about my answer for #3.
ReplyDeleteAlthough, I will keep working on #4 and 2.
2) 16+2√15-8√2y
ReplyDeleteHint: Problem 3
ReplyDeleteGiven:
3z = 5m
7j = 3m
__ j = 36z
We know that 36z = 60m. Go from there.
Solutions
ReplyDelete1. 60 × 2 = 120
Since no one wanted to buy it at that price, we reduce it by 60%.
120 × 0.4 = 48
We account for tax.
48 × 1.07 = $51.36
2. xy = 30
x + y = 16
x – y = ?
From the second equation, x = 16 – y.
Substitute into the first equation: (16 – y)(y) = 30
We have -y² + 16y = 30
y² – 16y + 30 = 0
Using the quadratic formula to solve:
x = [-b ± √(b² – 4ac)] ÷ 2a
For this case, a = 1, b = -16, and c = 30
x = [16 ± √(256 – 120)] ÷ 2 = (16 ± √136) ÷ 2 = 8 ± √34
Giving us two roots whose difference is:
(8 + √34) – (8 – √34) = 2√34
I didn’t mean to give you such a difficult problem. :-(
3. We will express joogs and zoogs in terms of 15 moogs.
15 moogs = 9 zoogs
15 moogs = 35 joogs
So, 9 zoogs = 35 joogs
36 zoogs would therefore be worth 35 × 4 = 140 joogs.
4. d = s × t
We write two equations:
d = 3(s + 25)
d = 4(s – 25)
Equate the expressions.
3s + 75 = 4s – 100
s = 175
Thus, d = 3(175 + 25) = 600 miles.
5. We want to add n such that the mean of {6, 11, 13, 7, 14, n} is n + 1.
(6 + 11 + 13 + 7 + 14 + n) ÷ 6 = n + 1
51 + n = 6n + 6
n = 9